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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math.special;
import org.apache.commons.math.MathException;
import org.apache.commons.math.util.FastMath;
/**
* This is a utility class that provides computation methods related to the
* error functions.
*
* @version $Revision: 1054186 $ $Date: 2011-01-01 03:28:46 +0100 (sam. 01 janv. 2011) $
*/
public class Erf {
/**
* Default constructor. Prohibit instantiation.
*/
private Erf() {
super();
}
/**
* <p>Returns the error function</p>
* <p>erf(x) = 2/√π <sub>0</sub>∫<sup>x</sup> e<sup>-t<sup>2</sup></sup>dt </p>
*
* <p>This implementation computes erf(x) using the
* {@link Gamma#regularizedGammaP(double, double, double, int) regularized gamma function},
* following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3)</p>
*
* <p>The value returned is always between -1 and 1 (inclusive). If {@code abs(x) > 40}, then
* {@code erf(x)} is indistinguishable from either 1 or -1 as a double, so the appropriate extreme
* value is returned.</p>
*
* @param x the value.
* @return the error function erf(x)
* @throws MathException if the algorithm fails to converge.
* @see Gamma#regularizedGammaP(double, double, double, int)
*/
public static double erf(double x) throws MathException {
if (FastMath.abs(x) > 40) {
return x > 0 ? 1 : -1;
}
double ret = Gamma.regularizedGammaP(0.5, x * x, 1.0e-15, 10000);
if (x < 0) {
ret = -ret;
}
return ret;
}
/**
* <p>Returns the complementary error function</p>
* <p>erfc(x) = 2/√π <sub>x</sub>∫<sup>∞</sup> e<sup>-t<sup>2</sup></sup>dt <br/>
* = 1 - {@link #erf(double) erf(x)} </p>
*
* <p>This implementation computes erfc(x) using the
* {@link Gamma#regularizedGammaQ(double, double, double, int) regularized gamma function},
* following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3).</p>
*
* <p>The value returned is always between 0 and 2 (inclusive). If {@code abs(x) > 40}, then
* {@code erf(x)} is indistinguishable from either 0 or 2 as a double, so the appropriate extreme
* value is returned.</p>
*
* @param x the value
* @return the complementary error function erfc(x)
* @throws MathException if the algorithm fails to converge
* @see Gamma#regularizedGammaQ(double, double, double, int)
* @since 2.2
*/
public static double erfc(double x) throws MathException {
if (FastMath.abs(x) > 40) {
return x > 0 ? 0 : 2;
}
final double ret = Gamma.regularizedGammaQ(0.5, x * x, 1.0e-15, 10000);
return x < 0 ? 2 - ret : ret;
}
}
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